A247135 Composite numbers for which the root mean square of proper divisors is an integer.

35, 49, 55, 145, 215, 341, 545, 589, 1189, 1681, 1769, 2449, 2641, 3005, 3131, 3599, 4681, 6931, 7601, 9899, 10469, 11215, 15871, 17639, 19511, 21691, 23711, 28345, 28369, 35429, 36521, 36811, 39059, 44609, 57121, 68189, 68759, 75349, 79921, 84419, 85801

Offset: 1

Author

Daniel Lignon, Nov 20 2014

Keywords

• nonn

Comments

Of course, for all prime numbers the mean square of proper divisors is an integer.

Examples

			35 is a term because it is not a prime, its proper divisors are {1, 5, 7} and sqrt((1^2 + 5^2 + 7^2)/3) = 5, an integer. - _Colin Barker_, Nov 20 2014
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..5000 (terms 1..100 from Daniel Lignon)

Crossrefs

Cf. A247142 (numbers for which the root mean square of proper divisors is an integer), A140480 (numbers for which the root mean square of all divisors is an integer) and A023884 (numbers for which the arithmetic mean of proper divisors is an integer).

Programs

Mathematica

Select[Range[2, 120000], (IntegerQ[RootMeanSquare[Most[Divisors[#]]]] && Not[PrimeQ[#]]) &]

PARI

s=[]; for(n=2, 120000, if(!isprime(n) && issquare((sigma(n, 2)-n^2)/(sigma(n, 0)-1)), s=concat(s, n))); s \\ Colin Barker, Nov 20 2014